Spin-selected electron transfer in liquid–solid contact electrification

Electron transfer has been proven the dominant charge carrier during contact electrification at the liquid–solid interface. However, the effect of electron spin in contact electrification remains to be investigated. This study examines the charge transfer between different liquids and ferrimagnetic solids in a magnetic field, focusing on the contribution of O2 molecules to the liquid–solid contact electrification. The findings reveal that magnetic fields promote electron transfer at the O2-containing liquid–solid interfaces. Moreover, magnetic field-induced electron transfer increases at higher O2 concentrations in the liquids and decreases at elevated temperatures. The results indicate spin-selected electron transfer at liquid–solid interface. External magnetic fields can modulate the spin conversion of the radical pairs at the O2-containing liquid and ferrimagnetic solid interfaces due to the Zeeman interaction, promoting electron transfer. A spin-selected electron transfer model for liquid–solid contact electrification is further proposed based on the radical pair mechanism, in which the HO2 molecules and the free unpaired electrons from the ferrimagnetic solids are considered radical pairs. The spin conversion of the [HO2• •e−] pairs is affected by magnetic fields, rendering the electron transfer magnetic field-sensitive.

where is the Bohr magneton, B is the external magnetic field and is the Boltzmann's constant. The population of the ↑↑ state exceeds that of the ↑↑ state by 0.46% at 293 K, which can be disregarded.

Supplementary Note 2
As shown in Fig. S6, when the O2 molecule interacts with the Fe 2+ ion on the Fe3O4 surface, the 3d 6 electrons belonging to the Fe 2+ ion transfer to the O2 molecule. During this process, the O2 molecule and the 3d 6 electron can be considered a triplet-radical pair, and the spin Hamiltonian can be expressed as follows: where − denotes the zero-field splitting in the O2 molecule, signifies the exchange interaction between the O2 molecule and Fe 2+ , and represents the Zeeman interaction, and, where ( ) is the exchange constant and r denotes the distance between the O2 molecule and Fe 2+ ion.
Here, the hyperfine interaction is disregarded since it is significantly smaller than the other terms.
The 3d 6 electron is considered a free radical, since the AC bias in the KPFM measurements unbinds the 3d 6 electrons from the solid surface, becoming dissolved electrons belonging to water clusters.
The three-electron system displays four quartet configurations and four doublet configurations, as follows: The spin conversion of the two quantum states depends on the difference between the energy levels of these two states and the corresponding off-diagonal matrix elements.
Here, it is considered that ( ) = 0. Therefore, the energy level of different spin states can be calculated as follows ( 2 and 3 4 are the g factors of the O2 molecule and Fe3O4, respectively.): ) The energy levels of all four quartet states contain the ± 1 3 term. For the O2 molecule, the D parameter value is about 3.5 cm -1 , which is significantly larger than the Zeeman term ( , where ≈ 2, = 0.927 × 10 −23 2 and = 0.5 ). The energy differences between the quartet and doublet states are not sensitive to the external magnetic field.
The corresponding off-diagonal matrix elements can be expressed as follows: It can be seen that all the off-diagonal matrix elements are either equal to zero or contain the D parameter (about 3.5 cm -1 ). The Zeeman term is equal to ∆ , which is several orders of magnitude smaller than the D parameter. The calculations show that both the energy differences between the quartet and doublet states and the corresponding off-diagonal matrix elements are not sensitive to magnetic fields. This suggests that the insufficient magnetic field sensitivity of the quartet-doublet spin conversion of the O2 molecule-3d 6 electron triplet-radical pair.

Supplementary Note 3
Supplementally note 2 considers the 3d 6 electron a free radical since the AC bias in the KPFM measurements unbinds the 3d 6 electrons from the solid surface, becoming dissolved electrons belonging to water clusters. Without the AC bias at the interface, the 3d 6 electrons in Fe3O4 are fixed by the exchange interactions. As shown in Fig. S6, the spin directions of the 3d 1~5 electrons are aligned by the magnetic field, while the 3d 6 electrons are antiparallel to the 3d 1~5 electrons, indicating that the 3d 6 electron spin is fixed to be antiparallel to the magnetic field. Therefore, when the 3d 6 electrons are antiparallel to the magnetic field, the energy level of the [HO2• •e − ] pair is substantially lower than when the 3d 6 electrons are parallel to the magnetic field. A spin Hamiltonian was constructed to describe this: where F is the fix constant. Its value is significantly larger than the thermal energy at 293 K, which is about 25 meV.
Therefore, the spin Hamiltonian of the [HO2• •e − ] pair can be expressed as follows: Here, it is considered that ( ) = 0. Therefore, the spin Hamiltonian can be expressed as follows: The constant F is much larger than when the magnetic field B is lower than 0.5 T.
Consequently, the effect of the magnetic field on the spin conversion of the [HO2• •e − ] pair can be disregarded.

Supplementary Note 4
The spin Hamiltonian of the radical pair considering the Zeeman interaction can be expressed as following: where 1 and 2 are the g factors of the two radicals in the radical pairs.
When we discuss the conversion of two spin states (state and state 0 ) of the radical pair, the wave function of the radical pair can be expressed as a mix state and it evolves with time, as following: And here is the time-dependent Schrodinger's equation: Integration of the above equation with * and 0 * gives the following results: Assuming that the initial spin state of the radical pair is singlet, which implies that | (0)| 2 = 1 and | 0 (0)| 2 = 0, then Equations S29 and S30 suggest that the spin states of the radical pairs convert between singlet state and triplet state at a angle frequency, in which = ∆ ħ . It can be seen that the S-T spin conversation rate of the radical pairs increases with the external magnetic field.

Supplementary Note 5
A cobalt alloy coated magnetic AFM probe (PPP-MFMR, NanoSensors) was used in the experiments.
The magnetic force between the magnetic tip and the Fe3O4 sample was detected directly by measuring the force-distance curve without a magnetic field, as shown in Fig. S10a. The forcedistance curve implied no significant magnetic force between the magnetic tip and magnetic sample without a magnetic field. However, when a magnetic field was applied, the probe was subjected to a significant magnetic force, even yielding a significant cantilever deflection under the magnetic field (0.5 T), which was observed via the photodetector. Therefore, the amplitude and phase of the probe vibration were significantly affected by the magnetic force, and the measured surface potential using a magnetic tip was far from the actual value, as shown in Fig. S10b (0.5 T). This was why a nonmagnetic tip was selected for testing.

Supplementary Note 6
The main scan in our experiments was performed in PeakForce tapping mode, which is a topography scanning mode developed by Bruker. In peakforce tapping mode, the tip contacts the sample surface point by point to record the profilometry, and the force curve is shown in Fig. S11a.
The tip approaches to the sample surface until the contact force reaches the set peakforce, and then, the tip is withdrawn from the sample surface. One of the biggest advantages of the PeakForce tapping mode is the ability to control the contact forces between tip and sample to the level of hundreds piconewton. In our experiments, the peakforce was set to 300 pN. Such a small contact force cannot lead to significant contact charge transfer between the metallic tip and the samples.
In order to verify that no transferred charge was introduced in PeakForce tapping mode for topography measurement, we use the PeakForce tapping mode to scan the sample surface trying to generate triboelectric charges (with 5 m scan size, 300 pN peakforce), and then, the surface potential of the scan area is detected in KPFM mode (10 m scan size). As shown in Figs. S11b, S11c, the results show that no triboelectric charges were introduced in PeakForce tapping mode, no matter in air or in DI water. Moreover, the tip used in experiments was nonmagnetic (SCM-PIT, Pt coated), which was not subjected to magnetic forces. As shown in Figs. S11d, S11e, there is no difference between the force-distance curves of the Pt coated tip on the Fe3O4 surface with and without a 0.5 T magnetic field, confirming that the tip is not subjected to magnetic force. Therefore, the enhancement in contact charge could not be from stronger interaction between tip and ferrite when magnetic field is applied.
For the tribovoltaic effect, two materials need to rub against each other to generate enough energy to excite electron-hole pairs. It is unlikely to generate a tribo-current at a slight contact in PeakForce tapping. As shown in Fig. S11f, no tribo-current was detected when the tip scans the Fe3O4 surface in PeakForce tapping mode. Therefore, the changes of the charge transfer at DI water and ferrimagnetic solid induced by magnetic field cannot be caused by the tribovoltaic effect.

Supplementary Note 7
The Ampere's force experienced by the Pt-coated AFM cantilever depended on the current through the cantilever (I), the length of the cantilever (L), and the external magnetic field (B), which is expressed as follows: where denotes the angle between the current and the magnetic field.
In the DH-KPFM system, the tip and sample electrode could be considered a capacitance, as shown in Fig. S12. The current through the cantilever could be calculated using the following equation: where Q denotes the induced charges on the tip and sample surfaces, V denotes the applied AC bias, and C denotes the capacitance between the tip and sample electrode. Equation S32 considered the capacitance of the tip-sample system a constant for convenience since the vibration amplitude of the tip was substantially smaller than the distance between the tip and sample electrode (lift high + thickness of the dielectric film) in the experiments.
The amplitude of the applied AC bias in the experiments was 1 V, and the frequency was 75 kHz, and the AC bias could be expressed as follows: = (2 × 7.5 × 10 4 ) The capacitance between the tip and the sample surface was systematically discussed in previous works. [50] In our experiments, the tip radius was less than 20 nm, and the distance between the tip and sample electrode was about 150 nm, so the capacitance between tip and sample electrode was less than 0.1 aF according to the results in Ref. 50. According to Equations S32 and S33, the current through the cantilever could be expressed as follows: = < 2 × 7.5 × 10 −15 (2 × 7.5 × 10 4 ) (S34) The highest magnetic field in our experiments was 0.5 T, the cantilever length was 225 m, and the current was perpendicular to the magnetic field. Therefore, the Ampere's force experienced by the Pt-coated AFM cantilever could be expressed as follows: < 0.5 × 225 × 10 −6 × 2 × 7.5 × 10 −15 (2 × 7.5 × 10 4 ) = 5.29 × 10 −18 (2 × 7.5 × 10 4 ) Such a small Ampere's force did not contribute to the resonance of the cantilever and could not influence the KPFM contact potential difference result.